Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices

G. Cipolloni, L. Erdös, Random Matrices: Theory and Application (2019).

Journal Article | Epub ahead of print | English
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Abstract
We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.
Publishing Year
Date Published
2019-05-09
Journal Title
Random Matrices: Theory and Application
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IST-REx-ID

Cite this

Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2019. doi:10.1142/S2010326320500069
Cipolloni, G., & Erdös, L. (2019). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. https://doi.org/10.1142/S2010326320500069
Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, 2019. https://doi.org/10.1142/S2010326320500069.
G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, 2019.
Cipolloni G, Erdös L. 2019. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application.
Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, World Scientific Publishing, 2019, doi:10.1142/S2010326320500069.

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